some stuff i know....
LRAM- left hand approximation. (this puts the rectangles used to find the area on the left side of the curve) x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation. (this puts the rectangles used to find the area on the right side of the curve) x[f(a+x)+...f(b)]
MRAM- approximation from the middle. (this puts the rectangles right on top of the curve, so that the curve goes through the middle of each one) x[f(mid)+f(mid)+...]
Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
Optimization can be used for finding the maximum/minimum amount of area of something. Steps in order to optimize anything:
1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is usually the other equation that ties in all the information given in the problem.
2. Solve the secondary equation for one variable and then plug that variable back into the primary. If the primary equation only have one variable you can skip this step.
3. Take the derivative of the primary equation after plugging in the variable, set it equal to zero, and then solve for the variable.
4. Plug that variable back into the secondary equation in order to solve for the last missing variable. Check endpoint if necessary to find the maximum or minimum answers
Substitution takes the place of the derivative rules for problems such as product rule and quotient rule. The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in
im not good at related rates and integrating a fraction.
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the steps for related rates are:
ReplyDelete1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
ok so related rates. first you have to figure out everything that is already given to you.
ReplyDeleteonce you have all that sorted out nicely, figure out what they are ASKING for you to FIND.
after that, i always look for the equation i will be using (for example, if they say, the volume of water in a conical tank is ...blah blah blah, then you would use the equation for volume of a cone)
then, plug everything in! also, remember if it says the rate at which the radius is changing, the would be dr/dt = whatever. if it says rate @ which volume is changing, dv/dt, rate @ which area is changing, da/dt, etc.
integrating a fraction can either be substitution or ln integration. i'm not sure how to tell when to use what though. and ln integration is fairly simple. it is ln(abs.value[bottom of fraction]) + c. also if you need to substitute in a 3 or something like that, just put 1/3 infront of the ln.
to integrate a fraction you usually gotta use substitution.
ReplyDeletesometimes it may be ln integration but why would we get that luckyyyy?